According to latest research on the dates of Saraswati river and Rama Setu, both these are older than 1700 BCE (NASA's research stated this and I don't currently have links to it.)Therefore ,it is incorrect to date Rig Veda, which existed prior to Rama Avatar, to 1700-1100 BC.
The currently-used savitR Gayatri Mantra was revealed to sage Viswamitra who pre-dated Rama. (Age of Rama Setu is >1,750,000 years, see here).
Prior to savitR (or Sun) gAyatri, people worshipped Indra gAyatri
And prior to Indra gAyatri, people worshipped brahma gAyatri.
Points 3 and 4 were researched and revealed by kAvya kanTha gaNapati muni.
In essence, it is not possible to date the gayatri mantra. We just need to remember that the Supreme pre-dates us and has continually manifested/revealed itself in various forms (mantra, avatAra etc.) since time immemorial. Modern science is too green and immature to help us understand what exists here and beyond. A lot more research by modern scientists (some of whom are rishis themselves - I consider Einstein, Bohr etc. rishis) is needed for us to even get some semblance of an understanding. kEnOpanishad states that brahman is beyond the known and the unknown. So it may very well be that science will never mature to a state where all is explained.